BIMSA > BIMSA-Tsinghua Seminar on Machine Learning and Differential Equations Deep Neural Network Algorithms for Oscillatory Flows, Causality Operators, and High Dimensional Fokker-Planck Equations
Deep Neural Network Algorithms for Oscillatory Flows, Causality Operators, and High Dimensional Fokker-Planck Equations
Organizers
Fan Sheng Xiong , Wu Yue Yang , Wen An Yong , Yi Zhu
Speaker
Wei Cai
Time
Thursday, October 13, 2022 10:15 AM - 11:15 AM
Venue
1129B
Online
Zoom 537 192 5549 (BIMSA)
Abstract
In this talk, we will present results on new types of deep neural networks (DNNs) in the following areas: (a) a multi-scale DNN method for solving highly oscillatory Navier-Stokes flows in complex domains (b) a causality DNN learning algorithm for operators in highly oscillatory function spaces encountered in seismic wave responses and other evolution PDEs systems with causalities; (c) a DNN based on forward and backward stochastic differential equations (FBSDEs) for high dimensional PDEs such as Fokker-Planck equations arising from statistical descriptions of biochemical systems, with application to compute committor functions and reaction rates in transition path sampling theory of complex chemical and biological systems.
Speaker Intro
Prof. Wei Cai is the Clements Chair Professor at the Department of Mathematics, Southern Methodist University, and he obtained his B.S. and M.S. in Mathematics from the University of Science and Technology of China in 1982 and 1985, respectively, and his Ph.D. in Applied Mathematics at Brown University in 1989. Before he joined SMU in 2017, he had been an assistant and then associate professor at the University of California at Santa Barbara during 1995-96, and a full Professor at the University of North Carolina, Charlotte after 1999. His research interest focuses on the development of deterministic, stochastic, and machine learning numerical methods for studying electromagnetic and quantum phenomena with applications in meta-materials, nano-photonics, nano-electronics, biological systems, and quantum systems. He has published over 130 refereed research articles and is the author of the book "Computational Methods for Electromagnetic Phenomena: electrostatics in solvation, scattering, and electron transport" published by Cambridge University Press in 2013. He was awarded the Feng Kang prize in scientific computing in 2005.